Nesting a stackpanel will cause the textbox to wrap properly:
<Viewbox Margin="120,0,120,0">
<StackPanel Orientation="Vertical" Width="400">
<TextBlock x:Name="subHeaderText"
FontSize="20"
TextWrapping="Wrap"
Foreground="Black"
Text="Lorem ipsum dolor, lorem isum dolor,Lorem ipsum dolor sit amet, lorem ipsum dolor sit amet " />
</StackPanel>
</Viewbox>